Chapter 5. Implementing Risk Forecasts (in MATLAB/Python)


Copyright 2011 - 2019 Jon Danielsson. This code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The GNU General Public License is available at: https://www.gnu.org/licenses/.


Listing 5.1/5.2: Download stock prices in MATLAB
Last updated August 2016

stocks = csvread('stocks.csv',1,0);
p1 = stocks(:,1);                   % consider first two stocks
p2 = stocks(:,2);
y1=diff(log(p1));                   % convert prices to returns
y2=diff(log(p2));
y1=y1(length(y1)-4100+1:end);       % length adjustment
y2=y2(length(y2)-4100+1:end);       % length adjustment
y=[y1 y2];
T=length(y1);
value = 1000;                       % portfolio value
p = 0.01;                           % probability
		
Listing 5.1/5.2: Download stock prices in Python
Last updated June 2018

import numpy as np
p = np.loadtxt('stocks.csv',delimiter=',',skiprows=1)
p = p[:,[0,1]]                                        # consider two stocks
## convert prices to returns, and adjust length
y1 = np.diff(np.log(p[:,0]), n=1, axis=0)
y2 = np.diff(np.log(p[:,1]), n=1, axis=0)
y1 = y1[len(y1)-4100:]
y2 = y2[len(y2)-4100:]
y = np.stack([y1,y2], axis = 1)
T = len(y1)
value = 1000                                          # portfolio value
p = 0.01                                              # probability
		

Listing 5.3/5.4: Univariate HS VaR in MATLAB
Last updated 2011

ys = sort(y1);       % sort returns
op = T*p;            % p percent smallest
VaR1 = -ys(op)*value
		
Listing 5.3/5.4: Univariate HS in Python
Last updated June 2018

ys = np.sort(y1)           # sort returns
op = int(T*p)              # p percent smallest
VaR1 = -ys[op - 1] * value
print(VaR1)
		

Listing 5.5/5.6: Multivariate HS VaR in MATLAB
Last updated 2011

w = [0.3; 0.7];       % vector of portfolio weights
yp = y*w;             % portfolio returns
yps = sort(yp);
VaR2 = -yps(op)*value
		
Listing 5.5/5.6: Multivariate HS in Python
Last updated June 2018

w = [[0.3], [0.7]]               # vector of portfolio weights
yp = np.squeeze(np.matmul(y, w)) # portfolio returns
yps = np.sort(yp)
VaR2= -yps[op - 1] * value
print(VaR2)
		

Listing 5.7/5.8: Univariate ES in MATLAB
Last updated 2011

ES1 = -mean(ys(1:op))*value
		
Listing 5.7/5.8: Univariate ES in Python
Last updated June 2018

ES1 = -np.mean(ys[:op]) * value
print(ES1)
		

Listing 5.9/5.10: Normal VaR in MATLAB
Last updated 2011

sigma = std(y1);                   % estimate volatility
VaR3 = -sigma * norminv(p) * value
		
Listing 5.9/5.10: Normal VaR in Python
Last updated June 2018

sigma = np.std(y1, ddof=1)                # estimate volatility
VaR3 = -sigma * stats.norm.ppf(p) * value
print(VaR3)
		

Listing 5.11/5.12: Portfolio normal VaR in MATLAB
Last updated 2011

sigma = sqrt(w' * cov(y) * w);       % portfolio volatility
VaR4 = - sigma * norminv(p) *  value
		
Listing 5.11/5.12: Portfolio normal VaR in Python
Last updated June 2018

## portfolio volatility
sigma = np.sqrt(np.mat(np.transpose(w))*np.mat(np.cov(y,rowvar=False))*np.mat(w))[0,0]
## Note: [0,0] is to pull the first element of the matrix out as a float
VaR4 = -sigma * stats.norm.ppf(p) * value
print(VaR4)
		

Listing 5.13/5.14: Student-t VaR in MATLAB
Last updated 2011

scy1=y1*100;                                   % scale the returns
res=mle(scy1,'distribution','tlocationscale');
sigma1 = res(2)/100;                           % rescale the volatility
nu = res(3);
VaR5 = - sigma1 * tinv(p,nu) * value
		
Listing 5.13/5.14: Student-t VaR in Python
Last updated June 2018

scy1 = y1 * 100                       # scale the returns
res = stats.t.fit(scy1)
sigma = res[2]/100                    # rescale volatility
nu = res[0]
VaR5 = -sigma*stats.t.ppf(p,nu)*value
print(VaR5)
		

Listing 5.15/5.16: Normal ES in MATLAB
Last updated June 2018

sigma = std(y1);
ES2=sigma*normpdf(norminv(p))/p * value
		
Listing 5.15/5.16: Normal ES in Python
Last updated June 2018

sigma = np.std(y1, ddof=1)
ES2 = sigma * stats.norm.pdf(stats.norm.ppf(p)) / p * value
print(ES2)
		

Listing 5.17/5.18: Direct integration ES in MATLAB
Last updated 2011

VaR = -norminv(p);
ES = -sigma*quad(@(q) q.*normpdf(q),-6,-VaR)/p*value
		
Listing 5.17/5.18: Direct integration ES in Python
Last updated June 2018

from scipy.integrate import quad
VaR = -stats.norm.ppf(p)
integrand = lambda q: q * stats.norm.pdf(q)
ES = -sigma * quad(integrand, -np.inf, -VaR)[0] / p * value
print(ES)
		

Listing 5.19/5.20: MA normal VaR in MATLAB
Last updated June 2018

WE=20;
for t=T-5:T
    t1=t-WE+1;
    window=y1(t1:t);                   % estimation window
    sigma=std(window);
    VaR6 = -sigma * norminv(p) * value
end
		
Listing 5.19/5.20: MA normal VaR in Python
Last updated June 2018

WE = 20
for t in range(T-5,T+1):
    t1 = t-WE
    window = y1[t1:t]                     # estimation window
    sigma = np.std(window, ddof=1)
    VaR6 = -sigma*stats.norm.ppf(p)*value
    print (VaR6)
		

Listing 5.21/5.22: EWMA VaR in MATLAB
Last updated 2011

lambda = 0.94;
s11 = var(y1(1:30));                              % initial variance
for t = 2:T
    s11 = lambda * s11  + (1-lambda) * y1(t-1)^2;
end
VaR7 = -norminv(p) * sqrt(s11) * value
		
Listing 5.21/5.22: EWMA VaR in Python
Last updated June 2018

lmbda = 0.94
s11 = np.var(y1[0:30], ddof = 1)             # initial variance
for t in range(1, T):
    s11 = lmbda*s11 + (1-lmbda)*y1[t-1]**2
VaR7 = -np.sqrt(s11)*stats.norm.ppf(p)*value
print(VaR7)
		

Listing 5.23/5.24: Two-asset EWMA VaR in MATLAB
Last updated 2011

s = cov(y);                                              % initial covariance
for t = 2:T
    s = lambda * s +  (1-lambda) * y(t-1,:)' * y(t-1,:);
end
sigma = sqrt(w' * s * w);                                % portfolio vol
VaR8 = - sigma * norminv(p) * value
		
Listing 5.23/5.24: Two-asset EWMA VaR in Python
Last updated June 2018

## s is the initial covariance
s = np.cov(y, rowvar = False)
for t in range(1,T):
    s = lmbda*s+(1-lmbda)*np.transpose(np.asmatrix(y[t-1,:]))*np.asmatrix(y[t-1,:])
sigma = np.sqrt((np.transpose(w)*s*w)[0,0])
## Note: [0,0] is to pull the first element of the matrix out as a float
VaR8 = -sigma * stats.norm.ppf(p) * value
print(VaR8)
		

Listing 5.25/5.26: GARCH in MATLAB
Last updated August 2016

[parameters,ll,ht]=tarch(y1,1,0,1);
omega = parameters(1)
alpha = parameters(2)
beta = parameters(3)
sigma2 = omega + alpha*y1(end)^2 + beta*ht(end) % calc sigma2 for t+1
VaR9 = -sqrt(sigma2) * norminv(p) * value
		
Listing 5.25/5.26: GARCH VaR in Python
Last updated June 2018

from arch import arch_model
am = arch_model(y1, mean = 'Zero', vol='Garch', p=1, o=0, q=1, dist='Normal')
res = am.fit(update_freq=5)
omega = res.params[0]
alpha = res.params[1]
beta = res.params[2]
## computing sigma2 for t+1
sigma2 = omega + alpha*y1[T-1]**2 + beta * res.conditional_volatility[-1]**2
VaR9 = -np.sqrt(sigma2) * stats.norm.ppf(p) * value
print(VaR9)
## Note: arch_model's GARCH optimization has issues with convergence